I find no indication of weight-limit recommendations for using Depo-Provera (injectable contraception) for birth control, but I suggest you ask your doctor about this.
Depo-Provera should not be used for longer than two years at a time because it can cause temporary bone loss that increases the longer it's used. Bone density generally returns to normal after injections are stopped, but the risk of fracture and osteoporosis may be increased if these injections are used for a long time. Here's some current related news:
Pros of Contraceptive Injection Outweigh Bone Risk
http://www.healthcentral.com/osteoporosis/news-263632-66.html
As with any treatment or drug, it's best to discuss the benefits and risks with your doctor, particularly how they might affect you individually. - MG